discrete probability distribution

Question

a lottery has three prizes: dollar 2000, 500 and 100. if there are 1300 tickets, and assuming all tickets are sold, what should the organizer charge for each ticket if the lottery is to be fair.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is recognizing that a “fair lottery” means that you need the price of the tickets to equal the expected value of winning a prize.

In this case we have total prize money of $2000 + $500 + $100 = $2600

And 1300 tickets sold

Meaning that a fair price for the ticket is $2600 / 1300 = $2.00 per ticket

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The total value of the prizes is 2000 + 500 + 100 = 2600.

2600/1300 = $2 per ticket. The total value of the tickets should equal the total value of the prizes.

In other words, if you bought all the tickets, the total value of the payouts should equal your cost.